document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5053>Question 5053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q. Prove the following identity: 1 divided by 1+cosx = 1/sin^2x - 1/sinxtanx<BR>\n" );
document.write( "I am at the dead end but these are my steps:<BR>\n" );
document.write( "R.S. <BR>\n" );
document.write( "1 divided by(sinx)(sinx)-1 divided by (sinx)(sinx/cosx)= <BR>\n" );
document.write( "sin^2x+cos^2x divided by sin^2x - sin^2x+cos^2xdivided by (sin^2x/cosx)=<BR>\n" );
document.write( "(sinx)(sinx)+(cosx)(cos)divided by (sinx)(sinx) - (sinx)(sinx) + (cosx)(cosx)(cosx)divided by (sinx)(sinx)=<BR>\n" );
document.write( "sin^2x + cos^2x - sin^2x + cos^2x(cosx) divided by (sinx)(sinx)= <BR>\n" );
document.write( "and here either <BR>\n" );
document.write( "1 - cosx divided by sin^2x<BR>\n" );
document.write( "or<BR>\n" );
document.write( "2cos^2x(cosx)divided by sin^2x<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "thanks mmm<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2520 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in any proof, pick one of the 2 sides and manipulate it until you get the other side. Always start with the more complicated side too!\r<BR>\n" );
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document.write( "Looking at your proof: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2Bcosx%29+=+1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinxtanx%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2Bcosx%29+=+1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinxtanx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the RighHand side looks more complicated, so i shall pick this..basically i have more things to work with...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinxtanx%29 ALIGN=MIDDLE  ALT=\"1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinxtanx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I shall use the facts that tanx = sinx/cosx and also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinx%2Asinx%2Fcosx%29 ALIGN=MIDDLE  ALT=\"1%2F%28sin%5E2%28x%29%29+-+1%2F%28sinx%2Asinx%2Fcosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sin%5E2%28x%29%29+-+cosx%2F%28sin%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sin%5E2%28x%29%29+-+cosx%2F%28sin%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cosx%29%2F%28sin%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+cosx%29%2F%28sin%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cosx%29%2F%281+-+cos%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+cosx%29%2F%281+-+cos%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now factorise the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cosx%29%2F%28%281+-+cosx%29%281+%2B+cosx%29%29 ALIGN=MIDDLE  ALT=\"%281+-+cosx%29%2F%28%281+-+cosx%29%281+%2B+cosx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281+%2B+cosx%29 ALIGN=MIDDLE  ALT=\"1%2F%281+%2B+cosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > QED\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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